Ultrasonic non-destructive evaluation (NDE) is a widely used technology used to evaluate quantitative properties of unknown surfaces such as thickness, shape, and texture. In ultrasonic pulse-echo methods, back-scattered echoes from the surface contain essential information pertaining to the properties of the reflector. Thus, it is desirable to correctly extract this information (e.g., in terms of amplitude, arrival time and center frequency). The parameters for time of arrival, amplitude and center frequency have been widely used in ultrasonic applications. For example, a technique in which backscattered echoes are modeled as superimposed Gaussian echoes corrupted by noise is known in the art. Additionally, Expectation Maximization (EM)-based algorithms for estimating ultrasonic signals have been developed. EM-based algorithms use the Gauss-Newton or the Levenberg-Marquart method to conduct an optimization search which is subject to the pitfall of landing in local minima.
To improve the success of these techniques, a suitable initial guess must be made for the parameters of the echo being sought. In many cases, the echo to be characterized is obscured by noise or a noisy baseline, which makes it difficult to form the initial guess. In response, there have been various pursuits centered around denoising a signal to facilitate easier characterization of the echo. A significant portion of these initiatives use first-order statistical methods such as averaging (e.g., stacking) to produce an estimate of a noisy baseline that contaminates a signal. First-order statistical methods work well to estimate a baseline when the variance of arrival times of the echoes in a gather is sufficiently large (such that the echo arrivals in the gather do not coincide). However, statistical methods have limitations when the echo arrivals do not follow a known distribution as statistical methods of the first-order, and even more elaborate statistical methods, are insufficient to address the challenge.